*4. Prove that 1³ +2³+ ... + n² = n²(n+1)² for all ne N.

Q: 1. Use the Newton's method to find the root of each of the following equations correct to 3 decimal…

A:

Q: 5. (a) Suppose 1 and Xn+1 = 2 Show that {n} converges and find the limit. X1 for all nEN.

A:

Q: Exercise 6.4 In problems 1-2, evaluate the integral (2) dz for the given function f 1 C 1.…

A: As per the policy, we are solving first question. Please repost it and specify which question is to…

Q: d² dy +5 dy + 5y = e-t sint, where y(0) = 0 and y' (0) = 1.

A: Given: The equation is d2ydt2+5dydt+5y=e-tsint. The given initial condition is y0=0 and y'0=1. To…

Q: 7. Alta Vista Co. employed 840 employees. It announced to layoff of the sales force. How many…

A: The total number of employees were 840 It announced to layoff 14 of the sales force. So, the number…

Q: Please write "True" or "False" in each empty box of the chart. For each box that is true, provide an…

A:

Q: Liva's Lumber, Inc., manufactures three types of plywood. The following table summarizes the…

A:

Q: b) Find the domain and the range of the following function: f(x)=√x²-25

A:

Q: Prove that 1-cos2x+sin2x 1+cos2x+sin2x = tan x

A:

Q: 2 Solve (x²D² - xD + 4) y = x² sin (log x).

A: Given differential equation is x2D2−xD+4y=x2sinlogx. We have to find the general solution of the…

Q: Why do you think someone might use a double negative? Do you think it is okay to use them in your…

A: For the solution of the problem follow the next step.

Q: 4. Show that if ki = (X; - X)/[Σ(X; – X)2], then (a) Σki = 0; = (b) Σk? = 1/[Σ(X; − x)2]; (c) Σκ;(X;…

A:

Q: 5.** There are n parking spots 1, 2,..., n on a one-way street. Cars 1,2,..., n arrive in this…

A: Given: Let the automobiles arrive in the designated parking spaces in the numbers 1, 2,..., n and…

Q: 1A. A pentagon, ABCDE, represents a plot of land and has the following vertices: 4(-1,0), B (3, 1).…

A: The equation of the x axis is y=0. If If the point: x, y is reflected about the line: y=0, then the…

Q: Q. 2. a) Find the limits of the following functions: lim sin 2x 52x² + x lim x²+12-4 x-2

A:

Q: You decide to work fewer hours per week, which results in a 19% decrease in your pay. What…

A:

Q: 1. Apply the the model function Gauss-Newton method to the least squares problem using for the data…

A:

Q: A force is specified by the vector F = [(-170)i + (120)j + (-80)k] N. Calculate the angles made by F…

A: Sol:- For positive x -axis:- Vector = (1,0,0) & GIVEN F = (-170, 120, -80) -170120-80,…

Q: find out whether the series given below converges or diverges E infinity/n=1 (n/5n+1)^n a) the…

A:

Q: Ax18x36=2592

A: Given equation is A×18×36=2592. We have to find the value of A. Divide both sides by 18×36 and…

Q: Find the Laplace transform of F(s) = = f(t) = = t 5

A:

Q: Prove that F^S is a vector space by verifying all of the axioms in the definition of vector spac

A:

Q: 12.1 x 302=

A:

Q: Let V: U → R be a strict Lyapunov function, where U CR" is a neighborhood of a compact and invariant…

A: Let V:U→R be a strict Lyapunov function, where U⊂ℝn is a neighborhood of a compact and invariant set…

Q: 45. Given the series to 8 decimal places? A. 5773 terms B. 8164 terms C. 9507 terms D. 16904 terms…

A: Given series is  ∑n=1∞ cosnπ3n2-5 Take cosnπ3n2-5 =an  then ∑n=1∞ cosnπ3n2-5 = ∑n=1∞ an   Note:- The…

Q: Q27. The value of lim x-0 (1+x)5-e5x+sin x² x2 is? →

A:

Q: 10 m 1º tam ² (²+3/-1) = 0 () If Stan cot 9r² + 3r − 1 n r=1 where m and n are co-prime, find the…

A:

Q: Consider the following statement: If m and n are odd integers then mn is odd. (1.1) Prove the above…

A:

Q: y" + 16y' = 128(t — 57/8); y(0) = 3, y' (0) = ( C

A:

Q: The mean and median both estimate the "average" of a sample. In 2020, the US mean and median net…

A: The mean is $53383 and median was $34612 We see that the mean is more than the median. When the mean…

Q: Find the solution of the equation a²z a²z + cos y ax² dy² which tends to zero as x→∞ and has the…

A: Given partial differential equation is ∂2z∂x2+∂2z∂y2=e−xcosy. It can be written as follows…

Q: The slope of the 4.0 kN force F is specified as shown in the figure. Express F as a vector in terms…

A:

Q: 120 students took part in a cross-country race. 30% of them finished the race within the qualifying…

A: The expression: "x% of y" is same as the expression: x×y100.

Q: Use power series expression to determine if sin 2 cosh 2 sinh: COS 2 is in general true. Show…

A: The power series expansion of the function sin z is:                          sin z= z-z33!+z55!- .…

Q: Population wealth as categorized by socioeconomic status classes (low, medium, high SES) is best…

A: An ordinal scale of measurement is a variable measurement  used represent the order of variables and…

Q: 1C. Triangle XYZ has cordinates X(-1, 3), (2, 5) and Z(-2,-3). Determine X Y Z' and X" Y" Z" if…

A: If the point: x, y is translated by the vector: ab, then the transformed point is x+a, y+b.

Q: Line integrals can look a lot alike! But they represent very different things. Consider: (i) [f ds…

A: Given That  Different Representation of Line Integral is as follows : i) ∫Cfdsii) ∫CF·driii) ∫nF·nds…

Q: Determine the partial differential equation by eliminating the arbitrary  function from the…

A: To Determine: The partial differential equation by eliminating the arbitrary function from the…

Q: 3. Express the principal value of 1n z in rectangular form. a) z = -5 b) z = -2 + j2 c) z = √2 + j√6…

A:

Q: If |A|= n, what is [P(A) — {{x} : x=A}|? -

A:

Q: Find a conformal map that takes {z|0<argz <} onto the unit disk.

A: Given that a conformal map that takes z | 0&lt;argz&lt;π8 onto the unit disk.

Q: Describe and graph (using a computer) the surfaces a) yz = 4 b) x² - y² = 1 c) 4x² + y² + 4z² − 4y −…

A: a) yz = 4  This represent the hyperbola. And  y = -4 , z = -1  y = -2, z = -2  y = -1, z = -4 y = 2…

Q: ion... Cour... (1) [2, 4] 19.85 The table shows the position of a motorcyclist after accelerating…

A:

Q: 1. Multiple Choice If D= [1, 2] × [01,02] then what does T(D) = {T(r,0)| (r,0) = D look like?

A:

Q: a tank is filled to capacity 30% .if we add 35 liters it goes to capacity 80% .what is the capacity…

A: It is given that the tank is filled to 30% capacity. Later, 35 litres added to the tank which…

Q: 5. Solve 6cos2x - 5sinx - 2 = 0 on the interval x € [0,2π]

A:

Q: 1. Apply the the model function Gauss-Newton method to the least squares problem using xit x2 + t…

A: Given below clear explanation

Q: A graphing calculator is recommended. The displacement (in centimeters) of a particle s moving back…

A:

Q: In Problems I through 20, find a particular solution y, of the given equation. In all these…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 6. Bill Murray purchased a bag of plain M&M's. The bag contained 55 candies. 50 were not green. In…

A: it is given that the bag contained 55 candies. 50 were not green. we need to find how many green…